Therefore, the non-classical correlations (local quantum uncertainty and local quantum Fisher information) upper bound the smallest possible variance of the estimator for interferometric phase estimations and thus yield these two inequalities [1]} :
\({\rm Var}\left(\theta \right)_{\rm min}\le \frac{1}{{\cal U}\left( \rho \right)},\hspace{28.45274pt}{\rm and}\hspace{28.45274pt} {\rm Var}\left(\theta \right)_{\rm min}\le \frac{1}{{\cal Q}_{F}\left(\rho \right)}.\) 
